A054683 Numbers whose sum of digits is even.

0, 2, 4, 6, 8, 11, 13, 15, 17, 19, 20, 22, 24, 26, 28, 31, 33, 35, 37, 39, 40, 42, 44, 46, 48, 51, 53, 55, 57, 59, 60, 62, 64, 66, 68, 71, 73, 75, 77, 79, 80, 82, 84, 86, 88, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 110, 112, 114, 116, 118, 121, 123, 125, 127, 129, 130

Offset: 1

Author

Odimar Fabeny, Apr 19 2000

Keywords

• nonn
• easy
• base

Comments

Union of A179082 and A179084; A179081(a(n)) = 0. - Reinhard Zumkeller, Jun 28 2010

Integers with an even number of odd digits. - Bernard Schott, Nov 18 2022

Examples

			0, 2, 4, 6, 8, 11 (2), 13 (4), 15 (6), 17 (8), 19 (10), 20 (2), 22 (4) and so on.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Index entries for 10-automatic sequences.
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A179081, A270264.

Subsequences: A014263, A099814, A179082, A179084.

Similar: A054684 (with an odd number of odd digits), A356929 (with an even number of even digits).

Programs

Mathematica

Select[Range[0,200],EvenQ[Total[IntegerDigits[#]]]&] (* Harvey P. Dale, Jan 04 2015 *)

PARI

is(n)=my(d=digits(n));sum(i=1,#d,d[i])%2==0 \\ Charles R Greathouse IV, Aug 09 2013

PARI

a(n) = n--; m = 10*(n\5); s=sumdigits(m); m + (1-(s-1)%2) + 2*(n%5) \\ David A. Corneth, Jun 05 2016

Python

A054683_list = [i for i in range(10**3) if not sum(int(d) for d in str(i)) % 2] # Chai Wah Wu, Mar 17 2016

Formula

a(n) = 2*n for the first 5 terms; a(n) = 2*n + 1 for the next 5 terms (recurrence).

I.e., for n > 0, a(n + 10) = a(n) + 20. - David A. Corneth, Jun 05 2016

Extensions

More terms from James Sellers, Apr 19 2000

Example corrected by David A. Corneth, Jun 05 2016